On Tuesday, Dodd denied to CNN that he had anything to do with adding the language, which has been used by officials at bailed-out insurance giant AIG to justify paying millions of dollars in bonuses to executives after receiving federal money.
He said Wednesday that the "grandfather clause" language "seemed like innocent modifications" at the time. Watch Dodd's interview with CNN's Dana Bash »
"I agreed reluctantly," Dodd said. "I was changing the amendment because others were insistent."
Dodd said he did not speak to high-ranking administration officials and the change came after his staff spoke with staffers from Treasury.
The White House did not immediately respond to CNN's request for comment.
At a town hall meeting in Costa Mesa, California, about an hour after Dodd spoke, President Barack Obama didn't directly address the language change -- but said he'll take responsibility for the bonuses being awarded.
"We didn't draft these contracts. We've got a lot on our plate. But it is appropriate when you're in charge to make sure stuff doesn't happen like this," he said. "So we're going to do everything that we can to fix it."
Dodd said later Wednesday in a written statement that his amendment allows the Treasury Department to review bonus contracts like AIG's and seek ways to get the money back for taxpayers.
AIG's derivatives branch is in Dodd's home state. Many of the bonuses in question were awarded to executives at that branch. But in the written statement, Dodd said he had no idea the legislation would impact the company.
"Let me be clear -- I was completely unaware of these AIG bonuses until I learned of them last week," he said.
Dodd also said in the statement that his comments on Tuesday and Wednesday to CNN did not conflict.
"I answered a question by CNN [Tuesday] night regarding whether or not [an exemption before] a specific date was aimed at protecting AIG," he said. "When I saw that my comments had been misconstrued, I felt it was important to set the record straight -- that this had nothing to do with AIG."
According to a transcript of the Tuesday interview, Dodd was asked about an executive-compensation provision "that exempts everything prior to February 11, 2009 -- any contracts prior to that date."
He said that language was not in the version of the bill that left the Senate and that he was not one of the negotiators who hammered out a compromise between the House and Senate versions of the plan.
"I can't point a finger at someone who offered a change at all," he said.
Asked whether he had later been able to figure out who added the language, he said, "I really don't know."
In Wednesday's interview, Dodd never said his Tuesday comments had been misunderstood.
"Going back and looking, I apologize," he said when questioned about his words from the day before.